• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.613-616
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• 2000

This paper considers the problem of subway crew scheduling. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper, we propose two basic techniques that solve the problem in a reasonable time, though the optimality of the solution is not guaranteed. To reduce the number of variables, we adopt column-generation technique. We could develop an algorithm that solves column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational results show column-generation makes the problem of treatable size, and variable fixing enables us to solve LP relaxation in shorter time without a considerable increase in the optimal value. Finally, we were able to obtain an integer optimal solution of a real instance within a reasonable time.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.410-417
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• 2002

We consider the constraint based explicit routing problem in MPLS based IP Network. In this problem, we are given a set of traffic demands and a network with different link capacities. The problem is to assign the demand commodities to the paths in the network while minimizing the maximum link load ratio. We formulate this problem as an integer programming problem and propose an efficient column generation technique. To strengthen the formulation, we consider some valid inequalities. We also incorporate the column generation technique with variable fixing scheme Computational results show that the algorithm gives high quality solutions in a short execution time.

• Management Science and Financial Engineering
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• v.11 no.2
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• pp.85-103
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• 2005

In this paper, we consider the routing and wavelength assignment problem in survivable WDM transport network without wavelength conversion. We assume the single-link failure and a path protection scheme in optical layer. When a physical network and a set of working paths are given, the problem is to select a link-disjoint protection path for each working path and assign a wavelength for each working and protection path. We give an integer programming formulation of the problem and propose an algorithm to solve it. Though the formulation has exponentially many variables, we solve the linear programming relaxation of it by using column generation technique. We devise a branch-and price algorithm to solve the column generation problem. After solving the linear programming relaxation, we apply a variable fixing procedure combined with the column generation to get an integral solution. We test the proposed algorithm on some randomly generated data and test results show that the algorithm gives very good solutions.

• Journal of the Korean Society for Railway
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• v.8 no.5
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• pp.391-397
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• 2005

In this paper we present a model for the maintenance routing construction and the trainset allocation (maintenance routing problem). The model solves the maintenance routing problem using column generation algorithm which was used to combine constraint programming and linear programming. Ilog-cplex was used to solve the linear programming model and Ilog-solver was used to solve the constraint programming model. The computational experience is also provided.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.389-392
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• 2004

The column generation process for the set-partitioning model of the vehicle routing problem requires repeated solutions of column generation subproblems which has a combinatorial structure similar to that of the traveling salesman problem. This limits the size of the problem that can be addressed. We introduce a new modeling approach, termed route-splitting, which splits each vehicle route into segments, and results in more tractable subproblems. A lower bounding scheme that yields an updated bound at each iteration of the column generation process is developed. Implementation issues, including a technique of controlling columns in the master problem, are explored. Lower bounds are computed on standard benchmark problems with up to 199 customers.

• Journal of the military operations research society of Korea
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• v.13 no.1
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• pp.101-115
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• 1987

This paper presents an optimization based heuristic algorithm for a tour bus scheduling problem where buses consist of various kinds of sightseeing and commutation services. First, this algorithm transforms the prolem into a vehicle routing problem on whose nodes denote trips and arcs denote connections between trips. Second, a greedy heuritic routing technique is applied to find a good feasible bus-route set. Then the greedy feasible solution is improved by the simplex method using column generation technique. The algorithm provides a better near-optimal solution which gives much reductions in the total tour distance and the number of tour buses.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2001.10a
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• pp.124-127
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• 2001

We consider the routing and wavelength assignment problem in survivable WDM transport network without wavelength conversion. We assume the single-link failure and a path protection scheme in optical layer. When a physical network and a set of working paths are given, the problem is to select a link-disjoint protection path for each working path and assign a wavelength for each working and protection path. We give an integer programming formulation of the problem and propose an algorithm to solve it based on column generation technique and variable fixing. We devise a branch-and-price algorithm to solve the column generation problem. We test the proposed algorithm on some randomly generated data and test results show that the algorithm gives very good solutions.

• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.4
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• pp.67-86
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• 2002

This paper considers subway crew scheduling problem. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper. we propose two basic techniques that solve the subway crew scheduling problem in a reasonable time, though the optimality of the solution is not guaranteed. We develop an algorithm that solves the column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational result for a real instance is reported.

• Journal of Korean Society of Transportation
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• v.26 no.2
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• pp.89-100
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• 2008

In an urban network controlled by traffic signals, there is an interaction between the signal timing and the routes chosen by individual road users. This study develops a bi level programming model for traffic signal optimization in networks with path based traffic assignment. In the bi level programming model, genetic algorithm approach has been proposed to solve upper level problem for a signalized road network. Path based traffic assignment using column generation technique which is proposed by M.H. Xu, is applied at the lower-level. Genetic Algorithm provieds a feasible set of signal timings within specified lower and upper bounds signal timing variables and feeds into lower level problem. The performance of this model is investigated in numerical experiment in a sample network. In result, optimal signal settings and user equilibrium flows are made.

• Management & Information Systems Review
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• v.29 no.4
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• pp.109-121
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• 2010

In this study, we propose a solution procedure to solve travelling salesman problem(TSP) with special cost function, route dependent travelling salesman problem(RDTSP). First, we develop an integer programming model to describe the problem. In the model, a variable means a possible route. And, the number of variables in this model are extremely large. So, we develop a LP relaxation problem of the IP model and solve the relaxation problem by a column generation technique. The relaxation problem does not guarantee the optimal solution. If we get an integer solution in the ralaxation problem, then the solution is an optimal one. But, if not, we cannot get an optimal solution. So, we approach a branch and price technique. The overall solution procedure can be applied a printed circuit board(PCB) assembly process.